Year 6: Changing metric units with decimals
Part of the Year 6 area, volume and measures chapter. Chapter overview · whole chapter on one page
Changing metric units with decimals
The metric units are linked by powers of ten. A kilometre is 1000 metres, a metre is 100 centimetres, and a metre is 1000 millimetres. Grams and kilograms work the same way, and so do litres and millilitres.
Going to a smaller unit makes the number bigger, so we multiply. Going to a bigger unit makes the number smaller, so we divide. Each power of ten moves the decimal point one place, so 1000 moves it three places.
Key ideas
- 1 km = 1000 m, 1 m = 100 cm, 1 m = 1000 mm, 1 cm = 10 mm.
- 1 kg = 1000 g, and 1 litre = 1000 ml.
- Smaller unit: the number gets bigger, so multiply.
- Bigger unit: the number gets smaller, so divide.
- Decimals work the same way: 0.725 litres = 725 ml, because 0.725 × 1000 = 725.
Key words. To convert means to change a measure into another unit. Kilo means 1000, so 1 km = 1000 m. Centi means one hundredth, so 1 m = 100 cm. Milli means one thousandth, so 1 m = 1000 mm.
Method. Find how many m make one km, then multiply by that number.
- Find how many m make one km. The table says 1 km = 1000 m.1 km = 1000 m
- Multiply by 1000. The answer is in m, which is smaller than km, so there are more m. Multiplying makes the number bigger.2.375 × 1000 = 2375
- Write the answer. Moving the decimal point 3 places to the right gives the answer in m.2375
Check. 2375 ÷ 1000 = 2.375, the number we started with. ✓
Watch out. A smaller unit gives a bigger number, so multiply. Move the decimal point to the right.
Key words. To convert means to change a measure into another unit. Kilo means 1000, so 1 km = 1000 m. Centi means one hundredth, so 1 m = 100 cm. Milli means one thousandth, so 1 m = 1000 mm.
Method. Find how many g make one kg, then divide by that number.
- Find how many g make one kg. The table says 1 kg = 1000 g.1 kg = 1000 g
- Divide by 1000. The answer is in kg, which is bigger than g, so there are fewer kg. Dividing makes the number smaller.4650 ÷ 1000 = 4.65
- Write the answer. Moving the decimal point 3 places to the left gives the answer in kg.4.65
Check. 4.65 × 1000 = 4650, the number we started with. ✓
Watch out. A bigger unit gives a smaller number, so divide. Move the decimal point to the left.
Key words. To convert means to change a measure into another unit. Kilo means 1000, so 1 km = 1000 m. Centi means one hundredth, so 1 m = 100 cm. Milli means one thousandth, so 1 m = 1000 mm.
Method. Find how many mm make one cm, then multiply by that number.
- Find how many mm make one cm. The table says 1 cm = 10 mm.1 cm = 10 mm
- Multiply by 10. The answer is in mm, which is smaller than cm, so there are more mm. Multiplying makes the number bigger.36.5 × 10 = 365
- Write the answer. Moving the decimal point 1 place to the right gives the answer in mm.365
Check. 365 ÷ 10 = 36.5, the number we started with. ✓
Watch out. A smaller unit gives a bigger number, so multiply. Move the decimal point to the right.
Watch out
Common mistake: 1 km is 1000 m, not 100 m. Check the direction. Metres are a smaller unit than kilometres, so 2.375 km gives a bigger number of metres. Grams are smaller than kilograms, so 4650 g gives a smaller number of kilograms.
Exam tip
Count the steps between the two units on the ladder, then move the decimal point that many places.
Exercise 9A Changing metric units
Non-calculatorKey words. To convert means to change a measure into another unit. Kilo means 1000, so 1 km = 1000 m. Centi means one hundredth, so 1 m = 100 cm. Milli means one thousandth, so 1 m = 1000 mm.
Method. Find how many m make one km, then multiply by that number.
- Find how many m make one km. The table says 1 km = 1000 m.1 km = 1000 m
- Multiply by 1000. The answer is in m, which is smaller than km, so there are more m. Multiplying makes the number bigger.3.2 × 1000 = 3200
- Write the answer. Moving the decimal point 3 places to the right gives the answer in m.3200
Check. 3200 ÷ 1000 = 3.2, the number we started with. ✓
Watch out. A smaller unit gives a bigger number, so multiply. Move the decimal point to the right.
Key words. To convert means to change a measure into another unit. Kilo means 1000, so 1 km = 1000 m. Centi means one hundredth, so 1 m = 100 cm. Milli means one thousandth, so 1 m = 1000 mm.
Method. Find how many cm make one m, then multiply by that number.
- Find how many cm make one m. The table says 1 m = 100 cm.1 m = 100 cm
- Multiply by 100. The answer is in cm, which is smaller than m, so there are more cm. Multiplying makes the number bigger.5.75 × 100 = 575
- Write the answer. Moving the decimal point 2 places to the right gives the answer in cm.575
Check. 575 ÷ 100 = 5.75, the number we started with. ✓
Watch out. A smaller unit gives a bigger number, so multiply. Move the decimal point to the right.
Key words. To convert means to change a measure into another unit. Kilo means 1000, so 1 km = 1000 m. Centi means one hundredth, so 1 m = 100 cm. Milli means one thousandth, so 1 m = 1000 mm.
Method. Find how many g make one kg, then multiply by that number.
- Find how many g make one kg. The table says 1 kg = 1000 g.1 kg = 1000 g
- Multiply by 1000. The answer is in g, which is smaller than kg, so there are more g. Multiplying makes the number bigger.0.6 × 1000 = 600
- Write the answer. Moving the decimal point 3 places to the right gives the answer in g.600
Check. 600 ÷ 1000 = 0.6, the number we started with. ✓
Watch out. A smaller unit gives a bigger number, so multiply. Move the decimal point to the right.
Key words. To convert means to change a measure into another unit. Kilo means 1000, so 1 km = 1000 m. Centi means one hundredth, so 1 m = 100 cm. Milli means one thousandth, so 1 m = 1000 mm.
Method. Find how many ml make one l, then multiply by that number.
- Find how many ml make one l. The table says 1 l = 1000 ml.1 l = 1000 ml
- Multiply by 1000. The answer is in ml, which is smaller than l, so there are more ml. Multiplying makes the number bigger.0.725 × 1000 = 725
- Write the answer. Moving the decimal point 3 places to the right gives the answer in ml.725
Check. 725 ÷ 1000 = 0.725, the number we started with. ✓
Watch out. A smaller unit gives a bigger number, so multiply. Move the decimal point to the right.
Key words. To convert means to change a measure into another unit. Kilo means 1000, so 1 km = 1000 m. Centi means one hundredth, so 1 m = 100 cm. Milli means one thousandth, so 1 m = 1000 mm.
Method. Find how many mm make one cm, then divide by that number.
- Find how many mm make one cm. The table says 1 cm = 10 mm.1 cm = 10 mm
- Divide by 10. The answer is in cm, which is bigger than mm, so there are fewer cm. Dividing makes the number smaller.480 ÷ 10 = 48
- Write the answer. Moving the decimal point 1 place to the left gives the answer in cm.48
Check. 48 × 10 = 480, the number we started with. ✓
Watch out. A bigger unit gives a smaller number, so divide. Move the decimal point to the left.
Key words. To convert means to change a measure into another unit. Kilo means 1000, so 1 km = 1000 m. Centi means one hundredth, so 1 m = 100 cm. Milli means one thousandth, so 1 m = 1000 mm.
Method. Find how many g make one kg, then divide by that number.
- Find how many g make one kg. The table says 1 kg = 1000 g.1 kg = 1000 g
- Divide by 1000. The answer is in kg, which is bigger than g, so there are fewer kg. Dividing makes the number smaller.750 ÷ 1000 = 0.75
- Write the answer. Moving the decimal point 3 places to the left gives the answer in kg.0.75
Check. 0.75 × 1000 = 750, the number we started with. ✓
Watch out. A bigger unit gives a smaller number, so divide. Move the decimal point to the left.
Key words. To convert means to change a measure into another unit. Kilo means 1000, so 1 km = 1000 m. Centi means one hundredth, so 1 m = 100 cm. Milli means one thousandth, so 1 m = 1000 mm.
Method. Find how many mm make one m, then multiply by that number.
- Find how many mm make one m. The table says 1 m = 1000 mm.1 m = 1000 mm
- Multiply by 1000. The answer is in mm, which is smaller than m, so there are more mm. Multiplying makes the number bigger.6.04 × 1000 = 6040
- Write the answer. Moving the decimal point 3 places to the right gives the answer in mm.6040
Check. 6040 ÷ 1000 = 6.04, the number we started with. ✓
Watch out. A smaller unit gives a bigger number, so multiply. Move the decimal point to the right.
Key words. To convert means to change a measure into another unit. Kilo means 1000, so 1 km = 1000 m. Centi means one hundredth, so 1 m = 100 cm. Milli means one thousandth, so 1 m = 1000 mm.
Method. Find how many ml make one l, then divide by that number.
- Find how many ml make one l. The table says 1 l = 1000 ml.1 l = 1000 ml
- Divide by 1000. The answer is in l, which is bigger than ml, so there are fewer l. Dividing makes the number smaller.1450 ÷ 1000 = 1.45
- Write the answer. Moving the decimal point 3 places to the left gives the answer in l.1.45
Check. 1.45 × 1000 = 1450, the number we started with. ✓
Watch out. A bigger unit gives a smaller number, so divide. Move the decimal point to the left.
Key words. To convert means to change a measure into another unit. Kilo means 1000, so 1 km = 1000 m. Centi means one hundredth, so 1 m = 100 cm. Milli means one thousandth, so 1 m = 1000 mm.
Method. Change the metres to centimetres first, so both lengths are in the same unit.
- Change 2.45 m to centimetres. There are 100 cm in 1 m, so we multiply by 100.2.45 × 100 = 245
- Take 85 cm away. The ribbon left is the whole length minus the piece cut off.245 - 85 = 160
- Write the answer. The answer is in centimetres.160
Check. 160 + 85 = 245 cm, which is 2.45 m. ✓
Watch out. Change the units before you subtract, so you do not mix metres and centimetres.
Key words. To convert means to change a measure into another unit. Kilo means 1000, so 1 km = 1000 m. Centi means one hundredth, so 1 m = 100 cm. Milli means one thousandth, so 1 m = 1000 mm.
Method. Change the kilograms to grams, then subtract the grams used.
- Change 1.25 kg to grams. There are 1000 g in 1 kg.1.25 × 1000 = 1250
- Take 375 g away. This is the flour that Mia used.1250 - 375 = 875
- Write the answer. The answer is in grams.875
Check. 875 + 375 = 1250 g, which is 1.25 kg. ✓
Watch out. Both amounts must be in grams before you subtract.
Key words. To convert means to change a measure into another unit. Kilo means 1000, so 1 km = 1000 m. Centi means one hundredth, so 1 m = 100 cm. Milli means one thousandth, so 1 m = 1000 mm.
Method. Change the litres to millilitres, then divide by the size of one cup.
- Change 0.75 litres to millilitres. There are 1000 ml in 1 litre.0.75 × 1000 = 750
- Divide by 50, the size of one cup. Each cup takes 50 ml, so count how many 50s there are.750 ÷ 50 = 15
- Write the answer. The answer is a number of cups.15
Check. 15 × 50 = 750 ml, which is 0.75 litres. ✓
Watch out. Change the litres first. Dividing 0.75 by 50 would give the wrong answer.
Key words. To convert means to change a measure into another unit. Kilo means 1000, so 1 km = 1000 m. Centi means one hundredth, so 1 m = 100 cm. Milli means one thousandth, so 1 m = 1000 mm.
Method. Change 0.4 km to metres, then compare it with 450 m.
- Change 0.4 km to metres. There are 1000 m in 1 km, so we multiply by 1000.0.4 × 1000 = 400
- Compare the two lengths. The question asks whether 0.4 km is more than 450 m.400 m and 450 m: 400 is less than 450
- Write the answer. Sam is not right.No
Check. 0.4 km is 400 m, which is 50 m less than 450 m. ✓
Watch out. Change the units first, then compare. Decimals can be misleading.